General Stmilartty Hypothests for Jet and Wake Flows 
and the continuity equation yields 
Yo ts vs 
x 
fe Ue u)y’dy + | Bel [oy - ue { var) dx =Hconst (3) 
0 al 0 
0 
provided the flow origin is excluded from this control volume. With 
w= Una. + ug one obtains for unconfined flow (dU,, /dx = 0) 
Yo 
2 j 
(us + uUee ) y'dy = 15 (4) 
0) 
This partial differential equation can be reduced to an ordinary dif- 
ferential equation by substituting the following similarity transfor - 
mation 
(4 + u gUee) /(U*6e) +U (x)U_)= f(n), with 
co 
which was introduced by Naudascher [6] ‘ 
Some algebraic manipulations yield the condition 
"No 
*2 
- H | 
are tn ony lie a a [ie = const (6) 
1 
0 
It should be remarked that in deriving Eq.6, the momentum equa- 
tion does not require further simplifications or restrictions as 
long as the special form of similarity expressed by Eq.5 is adopt- 
ed. 
To solve for the velocity and length scales U™*(x) anal (x) 
one must look for an additional information, The energy equation is 
chosen here, following the example of Wieghardt [9] and Liepmann 
and Laufer [10] . After substituting the same boundary-layer appro- 
ximations as in the equation of motion, the energy equation becomes 
ou wv = ge Os 
head 
= SE uy? aly t/p) (7) 
oy 
1289 
